An internal combustion engine which can change over from a lean air-fuel ratio combustion to a normal stoichiometric air-fuel ratio combustion is known. When an automatic transmission is combined with such an internal combustion engine, the automatic transmission is down-shifted by a normal shift control as soon as acceleration is required in the lean air-fuel ratio combustion region in which an extra driving force is small, and thus driveability deteriorates. To solve this problem, it is proposed that the down-shifting control of the automatic transmission in the lean air-fuel ratio combustion is prohibited for a predetermined period. (Refer to Japanese Unexamined Patent Publication Nos. 6-249012, 2000-52817 and 2-197431.)